Finite Group Databasebeta

← #26224131

Subgroups — #26224131

Order 12032.

730 conjugacy classes of subgroups.

The subgroup lattice has 638 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20252329C211yesmaximal, characteristic, complemented
2#20251816C211yesmaximal, characteristic
3#20244333C211yesmaximal, characteristic, complemented
4#20244164C211yesmaximal, characteristic, complemented
5#20243989C211yesmaximal, characteristic, complemented
6#20243989C211yesmaximal, characteristic, complemented
7#20243665C211yesmaximal, characteristic
8#20243665C211yesmaximal, characteristic
9#20243408C211yesmaximal, characteristic
10#20243274C211yesmaximal, characteristic, complemented
11#20243269C211yesmaximal, characteristic, complemented
12#20243265C211yesmaximal, characteristic, complemented
13#20243235C211yesmaximal, characteristic
14#20243228C211yesmaximal, characteristic
15C47×#3076C211yesmaximal, characteristic
16C2×#13094031C2211yescharacteristic
17C2×#13094031C2211yescharacteristic
18#15689254—21no—
19#15689254—21no—
20#15689254—21no—
21#15689254—21no—
22C2×#13093960C2211yescharacteristic
23C2×#13093960C2211yescharacteristic
24#15689150C2211yescharacteristic
25#15689150C2211yescharacteristic
26#15689147C2211yescharacteristic
27C2×#13093951C2211yescharacteristic
28C2×#13093951C2211yescharacteristic
29#15689079—21no—
30#15689079—21no—
31#15689079C2211yescharacteristic
32#15689079C2211yescharacteristic
33#15689079C2211yescharacteristic
34#15689079C2211yescharacteristic
35C4×#10625329—21no—
36C4×#10625329C2211yescharacteristic
37C2×#13093935—21no—
38C2×#13093935C2211yescharacteristic
39C2×#13093934C2211yescharacteristic
40C2×C8×Dic47C2211yescharacteristic
41C4×C4⋊Dic47C2211yescharacteristic
42#15688888C2211yescharacteristic
43#15688888C2211yescharacteristic
44#15688882C2211yescharacteristic
45#15688882C2211yescharacteristic
46#15688882C2211yescharacteristic
47#15688882C2211yescharacteristic
48#15688882C2211yescharacteristic
49#15688882C2211yescharacteristic
50#15688877C2211yescharacteristic
51#15688877C2211yescharacteristic
52C47×#533C2211yescharacteristic
53C4×#41×C47C2211yescharacteristic
54C47×#479C411yescharacteristic, complemented
55C47×#479C411yescharacteristic, complemented
56C47×#478C411yescharacteristic, complemented
57C47×#478C411yescharacteristic, complemented
58C47×#477C411yescharacteristic, complemented
59C47×#476C411yescharacteristic, complemented
60C47×#475C411yescharacteristic, complemented
61C47×#474C411yescharacteristic, complemented
62C47×#427C2211yescharacteristic
63C47×#427C2211yescharacteristic
64C2×C4⋊C8×C47C2211yescharacteristic
65C47×#416C2211yescharacteristic
66C47×#416C2211yescharacteristic
67#13094031—22no—
68#13094031—22no—
69#13094031—22no—
70#13094031Q814yescomplemented
71C2×#10625329—21no—
72C2×#10625329—21no—
73C2×#10625329C2311yescharacteristic
74C2×#10625329C2311yescharacteristic
75C2×#10625329C2311yescharacteristic
76C2×#10625329C2311yescharacteristic
77C22×C47⋊C8—21no—
78C22×C47⋊C8—21no—
79C22×C47⋊C8C2311yescharacteristic
80C22×C47⋊C8C2311yescharacteristic
81C2×C4⋊Dic47—21no—
82C2×C4×Dic47C2311yescharacteristic
83C2×C4×Dic47C2311yescharacteristic
84#13093960—22no—
85#13093960—22no—
86C4⋊(C47⋊C8)—21no—
87C4⋊(C47⋊C8)—21no—
88C4⋊(C47⋊C8)—21no—
89C4⋊(C47⋊C8)—21no—
90C4⋊(C47⋊C8)—21no—
91C4⋊(C47⋊C8)—21no—
92#13093951—22no—
93#13093951—22no—
94#13093935—21no—
95#13093935—21no—
96#13093935—21no—
97#13093935—21no—
98#13093935—21no—
99#13093935D411yescharacteristic
100#13093935D411yescharacteristic
101#13093935D411yescharacteristic
102#13093935D411yescharacteristic
103#13093934—22no—
104C4×C47⋊C8—21no—
105C4×C47⋊C8—21no—
106C4×C47⋊C8—21no—
107C4×C47⋊C8—21no—
108C4×C47⋊C8—21no—
109C8×Dic47—22no—
110C47⋊#95—21no—
111C2×#41×C47C2311yescharacteristic
112C22×C8×C47C2311yescharacteristic
113C22×C8×C47C2311yescharacteristic
114C4⋊Q8×C47C2×C411yescharacteristic
115C4⋊Q8×C47C2×C411yescharacteristic
116#125×C47C2×C411yescharacteristic
117#125×C47C2×C411yescharacteristic
118C22⋊Q8×C47—21no—
119C22⋊Q8×C47—21no—
120C4×Q8×C47—21no—
121C4×Q8×C47—21no—
122C4×Q8×C47C2×C411yescharacteristic
123C4×Q8×C47C2×C411yescharacteristic
124C4×D4×C47—21no—
125C4×D4×C47—21no—
126C4×D4×C47C2×C411yescharacteristic
127C4×D4×C47C2×C411yescharacteristic
128#117×C47—21no—
129#117×C47C2311yescharacteristic
130#117×C47C2311yescharacteristic
131#117×C47C2311yescharacteristic
132C2×C42×C47—21no—
133C2×C42×C47C2311yescharacteristic
134#107×C47C2×C411yescharacteristic
135#107×C47C2×C411yescharacteristic
136#107×C47C2×C411yescharacteristic
137#107×C47C2×C411yescharacteristic
138#106×C47C2×C411yescharacteristic
139#106×C47C2×C411yescharacteristic
140#106×C47C2×C411yescharacteristic
141#106×C47C2×C411yescharacteristic
142C4⋊C8×C47C2×C411yescharacteristic
143C4⋊C8×C47C2×C411yescharacteristic
144C4⋊C8×C47C2×C411yescharacteristic
145C4⋊C8×C47C2×C411yescharacteristic
146#103×C47C2×C411yescharacteristic
147#103×C47C2×C411yescharacteristic
148#103×C47C2×C411yescharacteristic
149#103×C47C2×C411yescharacteristic
150#102×C47C2×C411yescharacteristic
151#102×C47C2×C411yescharacteristic
152#102×C47C2×C411yescharacteristic
153#102×C47C2×C411yescharacteristic
154#41×C47—21no—
155#41×C47—21no—
156#41×C47C2×Q812yes—
157#41×C47#4112yes—
158C2×Q8×C47—21no—
159C2×Q8×C47—21no—
160C2×Q8×C47C22×C411yescharacteristic
161C2×D4×C47—21no—
162C2×D4×C47C22×C411yescharacteristic
163C22×C4×C47—21no—
164C22×C4×C47—21no—
165C22×C4×C47—21no—
166C22×C4×C47#4111yescharacteristic
167C22×C4×C47#4111yescharacteristic
168C22×C4×C47C2411yescharacteristic
169C22×Dic47—21no—
170C22×Dic47—21no—
171C2×C8×C47—21no—
172C2×C8×C47—21no—
173C2×C8×C47—21no—
174C2×C8×C47—21no—
175C2×C8×C47C22×C411yescharacteristic
176C2×C8×C47C22×C411yescharacteristic
177C2×C8×C47C22×C411yescharacteristic
178C2×C8×C47C22×C411yescharacteristic
179C4⋊C4×C47—21no—
180C4⋊C4×C47—21no—
181C4⋊C4×C47—21no—
182C4⋊C4×C47—21no—
183C4⋊C4×C47—21no—
184C4⋊C4×C47—21no—
185C4⋊C4×C47—21no—
186C4⋊C4×C47—21no—
187C4⋊C4×C47C22×C411yescharacteristic
188C4⋊C4×C47C22×C411yescharacteristic
189C4⋊C4×C47C22×C411yescharacteristic
190C4⋊C4×C47C22×C411yescharacteristic
191C4⋊C4×C47C22×C411yescharacteristic
192C4⋊C4×C47C22×C411yescharacteristic
193C22⋊C4×C47—21no—
194C22⋊C4×C47—21no—
195C22⋊C4×C47—21no—
196C22⋊C4×C47—21no—
197C22⋊C4×C47—21no—
198C42×C47—21no—
199C42×C47—21no—
200C42×C47—21no—
201C42×C47—21no—
202C42×C47—21no—
203C42×C47C22×C411yescharacteristic
204C42×C47C22×C411yescharacteristic
205C42×C47C2×D411yescharacteristic
206C42×C47C2×D411yescharacteristic
207C4⋊Dic47—42no—
208C4×Dic47—21no—
209C4×Dic47—21no—
210C4×Dic47—21no—
211C4×Dic47—21no—
212#10625329—24no—
213#10625329—21no—
214#10625329—21no—
215#10625329—24no—
216#10625329—21no—
217#10625329—21no—
218#10625329—21no—
219#10625329—21no—
220#10625329C2×Q812yes—
221#10625329#4112yes—
222C2×C47⋊C8—24no—
223C2×C47⋊C8—21no—
224C2×C47⋊C8—21no—
225C2×C47⋊C8—21no—
226C2×C47⋊C8—21no—
227C2×C47⋊C8—24no—
228C2×C47⋊C8—21no—
229C2×C47⋊C8—21no—
230C2×C47⋊C8C2×D411yescharacteristic
231C2×C47⋊C8C2×D411yescharacteristic
232C2×C47⋊C8C2×D411yescharacteristic
233C2×C47⋊C8C2×D411yescharacteristic
234C2×C47⋊C8C2×Q812yes—
235C2×C47⋊C8#4112yes—
236C23×C47—21no—
237C23×C47C2×#4111yescharacteristic
238Q8×C47—21no—
239Q8×C47—81no—
240Q8×C47—81no—
241Q8×C47C4×Q812yes—
242D4×C47—22no—
243D4×C47—22no—
244D4×C47—21no—
245D4×C47C4×Q812yes—
246C2×C4×C47—21no—
247C2×C4×C47—22no—
248C2×C4×C47—22no—
249C2×C4×C47—21no—
250C2×C4×C47—21no—
251C2×C4×C47—21no—
252C2×C4×C47—21no—
253C2×C4×C47—21no—
254C2×C4×C47—21no—
255C2×C4×C47—41no—
256C2×C4×C47—41no—
257C2×C4×C47—81no—
258C2×C4×C47—81no—
259C2×C4×C47C4×D411yescharacteristic
260C2×C4×C47C4×D411yescharacteristic
261C2×C4×C47C4×D411yescharacteristic
262C2×C4×C47C4×D411yescharacteristic
263C2×C4×C47C23×C411yescharacteristic
264C2×C4×C47C22×D411yescharacteristic
265C2×C4×C47C22×Q811yescharacteristic
266C2×C4×C47C2×#4111yescharacteristic
267C2×C4×C47C2×#4111yescharacteristic
268C2×C4×C47C2×#4111yescharacteristic
269C2×Dic47—22no—
270C2×Dic47—41no—
271C2×Dic47—41no—
272C2×Dic47—41no—
273C2×Dic47—41no—
274C2×Dic47—41no—
275C8×C47—21no—
276C8×C47—21no—
277C8×C47—21no—
278C8×C47—21no—
279C47⋊C8—22no—
280C47⋊C8—21no—
281C47⋊C8—22no—
282C47⋊C8—21no—
283C47⋊C8—41no—
284C47⋊C8—41no—
285C47⋊C8C22⋊Q812yes—
286C47⋊C8C22⋊Q812yes—
287#21629—471nomaximal, Sylow
288C22×C47—21no—
289C22×C47—21no—
290C22×C47—22no—
291C22×C47—41no—
292C22×C47—41no—
293C22×C47C2×C4×D411yescharacteristic
294C22×C47#52911yescharacteristic
295C22×C47#53311yescharacteristic
296C4×C47—21no—
297C4×C47—21no—
298C4×C47—21no—
299C4×C47—21no—
300C4×C47—22no—
301C4×C47—41no—
302C4×C47—41no—
303C4×C47—41no—
304C4×C47—41no—
305C4×C47—41no—
306C4×C47—41no—
307C4×C47C2×C4×Q811yescharacteristic
308C4×C47C4×#4111yescharacteristic
309C4×C47C2×C22⋊Q811yescharacteristic
310C4×C47#52511yescharacteristic
311Dic47—42no—
312Dic47—81no—
313#3076D4711yescharacteristic
314#2961—471no—
315#2875—471no—
316#1986—471no—
317#1950—471no—
318#1922—471no—
319#1922—471no—
320#1866—471no—
321#1866—471no—
322#1806—471no—
323#1773—471no—
324#1772—471no—
325#1771—471no—
326#1765—471no—
327#1764—471no—
328C2×C47—21no—
329C2×C47—21no—
330C2×C47—42no—
331C2×C47C4×C22⋊Q811yescharacteristic
332C2×C47#295611yescharacteristic
333C2×C47#295711yescharacteristic
334C2×#131—471no—
335C2×#131—471no—
336#533C2×D4711yescharacteristic
337C4×#41C2×D4711yescharacteristic
338#479Dic4711yescharacteristic, complemented
339#479Dic4711yescharacteristic, complemented
340#478Dic4711yescharacteristic, complemented
341#478Dic4711yescharacteristic, complemented
342#477Dic4711yescharacteristic, complemented
343#476Dic4711yescharacteristic, complemented
344#475Dic4711yescharacteristic, complemented
345#474Dic4711yescharacteristic, complemented
346#446—941no—
347#446—941no—
348#446—941no—
349#446—941no—
350C2×#108—471no—
351C2×#108—471no—
352#427C2×D4711yescharacteristic
353#427C2×D4711yescharacteristic
354#424—471no—
355#424—471no—
356#423—471no—
357C2×C4⋊C8C2×D4711yescharacteristic
358C2×#104—471no—
359C2×#104—471no—
360#416C2×D4711yescharacteristic
361#416C2×D4711yescharacteristic
362#405—471no—
363#405—471no—
364#405—471no—
365#405—471no—
366#405—941no—
367#405—941no—
368C4×M16—471no—
369C4×M16—941no—
370C2×#97—471no—
371C2×#97—471no—
372C2×#97—941no—
373C2×C4×C8—471no—
374C4×C4⋊C4—471no—
375#341—471no—
376#341—471no—
377#339—471no—
378#339—471no—
379#339—471no—
380#339—471no—
381#339—471no—
382#339—471no—
383#336—471no—
384#336—471no—
385C47#2162911yescharacteristic, complemented, Sylow
386C2×#41C22×D4711yescharacteristic
387#131—474no—
388#131—942no—
389#131—942no—
390#131—942no—
391C2×M16—471no—
392C2×M16—471no—
393C2×M16—471no—
394C2×M16—471no—
395C2×M16—941no—
396C2×M16—941no—
397C22×C8—471no—
398C22×C8—471no—
399C22×C8—941no—
400C22×C8—941no—
401C22×C8C22×D4711yescharacteristic
402C22×C8C22×D4711yescharacteristic
403C4⋊Q8C2×Dic4711yescharacteristic
404C4⋊Q8C2×Dic4711yescharacteristic
405#125C2×Dic4711yescharacteristic
406#125C2×Dic4711yescharacteristic
407C22⋊Q8—21no—
408C22⋊Q8—21no—
409C4×Q8—21no—
410C4×Q8—21no—
411C4×Q8C2×Dic4711yescharacteristic
412C4×Q8C2×Dic4711yescharacteristic
413C4×D4—21no—
414C4×D4—21no—
415C4×D4C2×Dic4711yescharacteristic
416C4×D4C2×Dic4711yescharacteristic
417#117—21no—
418#117C22×D4711yescharacteristic
419#117C22×D4711yescharacteristic
420#117C22×D4711yescharacteristic
421C2×C4⋊C4—941no—
422C2×C42—21no—
423C2×C42—471no—
424C2×C42—471no—
425C2×C42C22×D4711yescharacteristic
426#108—942no—
427#108—942no—
428#107C2×Dic4711yescharacteristic
429#107C2×Dic4711yescharacteristic
430#107C2×Dic4711yescharacteristic
431#107C2×Dic4711yescharacteristic
432#106C2×Dic4711yescharacteristic
433#106C2×Dic4711yescharacteristic
434#106C2×Dic4711yescharacteristic
435#106C2×Dic4711yescharacteristic
436C4⋊C8—941no—
437C4⋊C8—941no—
438C4⋊C8—941no—
439C4⋊C8—941no—
440C4⋊C8—941no—
441C4⋊C8—941no—
442C4⋊C8C2×Dic4711yescharacteristic
443C4⋊C8C2×Dic4711yescharacteristic
444C4⋊C8C2×Dic4711yescharacteristic
445C4⋊C8C2×Dic4711yescharacteristic
446#104—942no—
447#104—942no—
448#103C2×Dic4711yescharacteristic
449#103C2×Dic4711yescharacteristic
450#103C2×Dic4711yescharacteristic
451#103C2×Dic4711yescharacteristic
452#102C2×Dic4711yescharacteristic
453#102C2×Dic4711yescharacteristic
454#102C2×Dic4711yescharacteristic
455#102C2×Dic4711yescharacteristic
456#97—471no—
457#97—471no—
458#97—471no—
459#97—471no—
460#97—941no—
461#97—941no—
462#97—941no—
463#97—941no—
464#97—942no—
465#97—941no—
466C4×C8—941no—
467C4×C8—941no—
468C4×C8—941no—
469C4×C8—941no—
470C4×C8—942no—
471C4×C8—941no—
472#95—941no—
473#41—21no—
474#41—21no—
475#41Q8×D4712yes—
476#41#1062535412yes—
477C2×Q8—21no—
478C2×Q8—21no—
479C2×Q8C22×Dic4711yescharacteristic
480C2×D4—21no—
481C2×D4C22×Dic4711yescharacteristic
482C22×C4—21no—
483C22×C4—21no—
484C22×C4—21no—
485C22×C4—941no—
486C22×C4—941no—
487C22×C4#1062535211yescharacteristic
488C22×C4#1062535211yescharacteristic
489C22×C4C23×D4711yescharacteristic
490M16—472no—
491M16—472no—
492M16—944no—
493M16—944no—
494M16—941no—
495M16—941no—
496M16—941no—
497M16—941no—
498M16—941no—
499M16—941no—
500C2×C8—21no—
501C2×C8—21no—
502C2×C8—21no—
503C2×C8—21no—
504C2×C8—471no—
505C2×C8—471no—
506C2×C8—472no—
507C2×C8—472no—
508C2×C8—471no—
509C2×C8—471no—
510C2×C8—944no—
511C2×C8—944no—
512C2×C8—941no—
513C2×C8—941no—
514C2×C8—941no—
515C2×C8—941no—
516C2×C8—941no—
517C2×C8—941no—
518C2×C8C22×Dic4711yescharacteristic
519C2×C8C22×Dic4711yescharacteristic
520C2×C8C22×Dic4711yescharacteristic
521C2×C8C22×Dic4711yescharacteristic
522C4⋊C4—21no—
523C4⋊C4—21no—
524C4⋊C4—21no—
525C4⋊C4—21no—
526C4⋊C4—21no—
527C4⋊C4—21no—
528C4⋊C4—21no—
529C4⋊C4—21no—
530C4⋊C4—1882no—
531C4⋊C4C22×Dic4711yescharacteristic
532C4⋊C4C22×Dic4711yescharacteristic
533C4⋊C4C22×Dic4711yescharacteristic
534C4⋊C4C22×Dic4711yescharacteristic
535C4⋊C4C22×Dic4711yescharacteristic
536C4⋊C4C22×Dic4711yescharacteristic
537C22⋊C4—21no—
538C22⋊C4—21no—
539C22⋊C4—21no—
540C22⋊C4—21no—
541C22⋊C4—21no—
542C42—21no—
543C42—21no—
544C42—21no—
545C42—21no—
546C42—21no—
547C42—941no—
548C42—941no—
549C42—941no—
550C42—941no—
551C42D4×D4711yescharacteristic
552C42D4×D4711yescharacteristic
553C42C22×Dic4711yescharacteristic
554C42C22×Dic4711yescharacteristic
555C23—21no—
556C23C2×#1062535211yescharacteristic
557Q8—21no—
558Q8—81no—
559Q8—81no—
560Q8Q8×Dic4712yes—
561D4—22no—
562D4—22no—
563D4—21no—
564D4Q8×Dic4712yes—
565C2×C4—21no—
566C2×C4—22no—
567C2×C4—22no—
568C2×C4—21no—
569C2×C4—21no—
570C2×C4—21no—
571C2×C4—21no—
572C2×C4—21no—
573C2×C4—21no—
574C2×C4—41no—
575C2×C4—41no—
576C2×C4—81no—
577C2×C4—81no—
578C2×C4—942no—
579C2×C4—1881no—
580C2×C4—1881no—
581C2×C4—1881no—
582C2×C4—1881no—
583C2×C4—1881no—
584C2×C4D4×Dic4711yescharacteristic
585C2×C4D4×Dic4711yescharacteristic
586C2×C4D4×Dic4711yescharacteristic
587C2×C4D4×Dic4711yescharacteristic
588C2×C4C23×Dic4711yescharacteristic
589C2×C4C2×D4×D4711yescharacteristic
590C2×C4C2×Q8×D4711yescharacteristic
591C2×C4#41×D4711yescharacteristic
592C2×C4#41×D4711yescharacteristic
593C2×C4C2×#1062535411yescharacteristic
594C8—21no—
595C8—21no—
596C8—21no—
597C8—21no—
598C8—472no—
599C8—472no—
600C8—942no—
601C8—941no—
602C8—941no—
603C8—942no—
604C8—1881no—
605C8—1881no—
606C22—21no—
607C22—21no—
608C22—22no—
609C22—41no—
610C22—41no—
611C22C2×D4×Dic4711yescharacteristic
612C22#1568965911yescharacteristic
613C22#1568967511yescharacteristic
614C4—21no—
615C4—21no—
616C4—21no—
617C4—21no—
618C4—22no—
619C4—41no—
620C4—41no—
621C4—41no—
622C4—41no—
623C4—41no—
624C4—41no—
625C4—3761no—
626C4—1882no—
627C4C2×Q8×Dic4711yescharacteristic
628C4#41×Dic4711yescharacteristic
629C4C22⋊Q8×D4711yescharacteristic
630C4#1568963611yescharacteristic
631C2—21no—
632C2—21no—
633C2—42no—
634C2C22⋊Q8×Dic4711yescharacteristic
635C2#2025229811yescharacteristic
636C2#2025230511yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D47
commutatorC2×C4×C47C23×C4
FrattiniC22×C4C23×D47
FittingC47×#3076C2
socleC22×C47C2×C4×D4
prime radicalC2×#41×C47C23
cosocleC22×C4×C47C24
hypercenter#3076D47
hypocenterC47#21629
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #3076

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. #20252329C2semidirect
3. #20244333C2semidirect
4. #20244164C2semidirect
5. #20243989C2semidirect
6. #20243989C2semidirect
10. #20243274C2semidirect
11. #20243269C2semidirect
12. #20243265C2semidirect
54. C47×#479C4semidirect
55. C47×#479C4semidirect
56. C47×#478C4semidirect
57. C47×#478C4semidirect
58. C47×#477C4semidirect
59. C47×#476C4semidirect
60. C47×#475C4semidirect
61. C47×#474C4semidirect
70. #13094031Q8semidirect
338. #479Dic47semidirect
339. #479Dic47semidirect
340. #478Dic47semidirect
341. #478Dic47semidirect
342. #477Dic47semidirect
343. #476Dic47semidirect
344. #475Dic47semidirect
345. #474Dic47semidirect
385. C47#21629semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#202523292
#202518162
#202443332
#202441642
#202439892
#202436652
#202434082
#202432742
#202432692
#202432652
#202432352
#202432282
C47×#30762
#2162947